The only shot i can give you is that you duplicated the app but not the data source, then when you changed the second app changed both apps.
You need to create one datsource for each client.
Hi Luciano - thanks for your reply. So, in terms of 'You need to create one datasource for each client' - will it suffice to duplicate the existing datasource, edit the duplicate to point to a different Google Analytics profile, and then delete the original datasource?
Yes, that's the idea.
Build one datasource for each client pointing to your respective file and publish them with different names.
I found this session at the Tableau Conference to be quite helpful. It might help you in terms of building a better process using scripts - Sign Up | Tableau Conference Live. The session title was "Bringing You Back from the Dark Side of XML Hacking with the Document API". If the link doesn't work for whatever reason, you can search on tclive.tableau.com